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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.2 Bogotá July/Dec. 2020 Epub Dec 05, 2020
https://doi.org/10.15446/rce.v43n2.79151
Original articles of research
Convergence Theorems in Multinomial Saturated and Logistic Models
Teoremas de convergencias en los modelos saturados y logísticos multinomiales
1Programa de ingeniería industrial, Facultad de ingeniería, Universidad Simón Bolívar, Barranquilla, Colombia
2Departamento de Matemáticas y Estadística, División de Ciencias Básicas, Universidad de Norte, Barranquilla, Colombia
3Departamento de Ciencias Básicas, Corporación Politécnico de la Costa Atlántica, Barranquilla, Colombia
In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demonstrated. Furthermore, properties are identified and, based on an asymptotic theory, convergence theorems are tested for score vectors and information matrices of both models. Finally, an application of this theory is presented and assessed using data from the R statistical program.
Key words: Multinomial logit model; Saturated model; Logistic regression; Maximum likelihood estimator; Score vector; Fisher information matrix
En este artículo se desarrolla un estudio teórico de los modelos logísticos y saturados multinomiales cuando la variable de respuesta toma uno de R ≥ 2 niveles. Se presentan y demuestran teoremas sobre la existencia y cálculos de las estimaciones de máxima verosimilitud (ML-estimaciones) de los parámetros de ambos modelos. Se encuentran sus propiedades y, usando teoría asintótica, se prueban teoremas de convergencia para los vectores de puntajes y para las matrices de información. Se presenta y analiza una aplicación de esta teoría con datos tomados de la librería aplore3 del programa R.
Palabras clave: Modelo logístico multinomial; Modelo saturado; Regresión logística; Estimador de máxima verosimilitud; Vector score; Matriz de información de Fisher
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Received: October 2019; Accepted: May 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
